Supporting Information for. Dependence of Avidity on Linker Length for a Bivalent Ligand-Bivalent Receptor Model System

Transcription

1 Supporting Information for Depenence of Aviity on Linker Length for a Bivalent Ligan-Bivalent Receptor Moel System Eric T. Mack, Phillip W. Snyer, Raquel Perez-Castillejos, Başar Bilgiçer, Demetri T. Moustakas, Manish J. Butte, an George M. Whitesies * Department of Chemistry an Chemical Biology, Harvar University Oxfor Street, Cambrige, MA 38 * Corresponence: gwhitesies@gmwgroup.harvar.eu Table of Contents Figure S... Pg. S Table S..... Pg. S4 Derivation of equation to fit the fluorescent isplacement assay... Pg. S5 Synthesis of (CA) Pg. S9 X-ray Data collection an processing.. Pg. S Molecular replacement... Pg. S Refinement.. Pg. S Table S. Pg. S References.. Pg. S3 S

2 Figure S. Seimentation equilibrium experiments of CA an (CA) with an without ae LRL as observe at 8 nm at 5 ºC. The hollow circles are experimental ata for an the line is the fit for a single ieal species. LEG 3 L LSar L S

3 LSar L LSar 4 L LSar 6 L LSar 8 L LEG L S3

4 Table S. The maximum istance between the two nitrogen atoms of the sulfonamie functional groups of the bivalent ligans (extene length, Γ, Å) an the estimate molecular weights (MW) for CA, (CA), an mixtures of (CA) an bivalent ligans etermine from seimentation equilibrium experiments. Proteins an complexes of imers an bivalent ligans Extene length of the linker, Г (Å) Estimate MW (kda) (95% CI) CA ( 3, 35 ) (CA) ( 54, 6 ) (CA) LEG 3 L 5 57 ( 5, 6 ) (CA) LSar L 3 57 ( 5, 6 ) (CA) LSar L ( 53, 6 ) (CA) LSar 4 L ( 53, 55 ) (CA) LSar 6 L ( 53, 63 ) (CA) LSar 8 L 6 59 ( 55, 63 ) (CA) LSar L 69 6 ( 57, 68 ) S4

5 Derivation of Mathematical Moel This section erives the equation use to fit the fluorescence isplacement ata. Figure S. Thermoynamic scheme escribing the bining of ligans to the imer of CA. These schemes escribe the efinition for the bining constants = (S) L ( / 4) lin (/ ) [I = (S) I lin L = (S3) L cyc S5

6 Figure 5. Thermoynamic scheme an simulations escribing the moel use to analyze the fluorescence titration experiments. L a) The thermoynamic scheme comprises three equilibria characterize by three equilibrium constants (,, an 3 ) an four species that contain a imer of CA. ethox 4 L I[I = = (S4) I L = = (S5) L I[I cyc (L ) = = (S6) L 3 cyc Rewriting the concentrations of the imer complexes in terms of the issociation constants, statistical factors, an the concentration of (CA) L I (eq S7-S9). [I I = L 4 I (S7) (L ) = L [I cyc L = L [I I I (S8) (S9) S6

7 At high concentrations of ansylamie () employe in these experiments; the total concentration of is assume equal to the free or unboun concentration (eq ). The mass-balance equations for imers an ligans (S-S) [I = [I (S) = L I (L ) L cyc (S) [CA = (I) L I (L ) L cyc (S) Replacing the complex (CA) L I with the variable B, for simplicity. We can express the massbalance equation for ligan an imer as functions of the issociation constants, statistical factors, B, [I, an (eq 3 an 4). = [B [I [I (S3) [CA 4 [I = in [I tra [B [I (S4) The combination of equations S, S3, an S4 yiels an expression (eq S5) for the concentration of free ligan,, that epens on the total concentrations of inhibitor, [I, ligan,, an imer, [CA, an on the equilibrium constants of the system,,, an. 3 [ [ L b[ L c L = a (S5) The coefficients a, b, an c for each term of the polynomial are efine by Equations S6-S8. S7

8 a = [I [CA [I [I [I (S6) b = (S7) 4 [I [CA [CA [I [I [I c = ([I 4 ) (S8) There exist three solutions to a cubic equation but only one of them is physically real it has no imaginary component (Equation S9) [ L R Q 3 R R Q R a = (S9) 3 3b a Q = 9 R = 9ab 7c a 54 3 The observe fluorescence signal can be escribe by a function of the concentration of imers. I [B Fl obs = ( Flmax Flmin ) Flmin (S) [CA Substituting the concentration of (CA) I (eq S7), an [B (eq S4) into equation S yiels an expression for the observe fluorescence that epens on the known total concentration of S8

9 [I an the varying concentration of free ligan, Fl [I obs Fl Fl [I 4 [I [I = Fl (S). ( max min ) min Substituting the value of free ligan (equation S9) in equation S yiels an expression for fluorescence that is a function of six parameters: the total concentrations of inhibitor, [I, ligan,, an imer,, an on the equilibrium constants of the system,,, an. The total concentrations are known, as they are chosen by the experimentalist. The issociation constants is the sole ajustable parameter to fit the experimental curves of the observe fluorescence. Synthesis of (CA) Methos for the overexpression in an purification of the HCAII ouble mutant (33C, C6S), mutant HCAII, from E. coli have been reporte previously. To a solution of mutant HCAII (.5 mg,.38 µmoles) in mm PBS (5. ml) at ph 7. was ae a solution of bismaleimiomethyl ether (4 µg,.7 µmoles) in like buffer (.85 ml) over the course of h in 8.5 µl equal portions. The volume of the crue reaction mixture was reuce to ml then purifie by size-exclusion chromatography using a column of Superex 75 (6 6 mm) eluting with mm PBS at a constant flow rate of.5 ml min -. The appropriate fractions were poole to yiel 8 mg (7 % yiel) of (CA). Purity an molecular weight were consistent with propose structure as assesse by SDS-PAGE. ESI-MS m/z foun 58,385 Da, calc. 58,386 Da (apo-p H O from the hyration of the maleimie). S9

10 Data collection an processing The intensity ata were processe an integrate with Mosfilm. Reflections were observe to.5 Å with measurement of 78.8% of all theoretical reflections (completeness), an a resolution cutoff was arbitrarily chosen for all further processing at.8 Å because the mean intensity/stanar ev = 3. at that resolution. Statistical analysis of the intensities with a Wilson plot [CCP4 program Wilson 3 reveale a mean isotropic temperature factor of. Å. Molecular replacement The structure was solve by molecular replacement, using HCAII from a publishe structure (PDB G5 4 ) as the search moel. All 58 resiues from the HCA search moel were use, incluing all sie chains. There was only one ominant solution foun with the CCP4 program Phaser 5. For this solution, the log likelihoo gain was Refinement The molecular replacement moel unerwent a rigi-boy minimization an a Cartesian simulate annealing uring which a bulk solvent correction was applie. Repeate cycles of refinement using CNS (Crystallography an NMR System) program 6 an manual rebuiling using MOLOC 7 followe to ensure that the free R-factor ecrease steaily. Refinement inclue positional refinement, Cartesian an torsional simulate annealing, an B-factor refinement with the maximum likelihoo target 8. The moel was refine against 9% of the measure ata between 3. an.4 Å using the Engh an Huber stereochemical ictionary. The remaining % of the ata were exclue from all refinement calculations to cross-valiate the progress of refinement (the free R set). After 5 cycles of refinement an manual rebuiling, water molecules were automatically ae to the structure provie that (a) ensity appeare S

11 >. ó on the Fo - Fc map, (b) they forme hyrogen bons of reasonable geometry, an (c) their inclusion reuce the free R-factor. The final R-factor was 4. an the free R-factor was 6.9, with excellent geometry. A Ramachanran plot reveale 97% of the resiues fall into allowe regions. The overall statistics for ata collection an refinement are summarize in Table S. To check for search moel bias, a high-temperature electron ensity omit map was calculate. It reveale that the main chain positions were similar between our structure an the search moel an that the sie chain conformations clearly support our structure versus that of the search moel. The imer mate falls across a crystallographic -fol symmetry axis. The structure of (CA) containe one molecule of HCA in the asymmetric unit. The methylmaleimie cross-linker connecte pairs of monomers; the ether oxygen of the crosslinker reste upon a crystallographic two-fol symmetry axis. Existing crystallography software oes not allow bone atoms, such as this oxygen, to lie exactly on a crystallographic axis, so bons to the ether oxygen were moele using fixe istance constraints. The crosslinking reaction, also, forme a iastereomeric mixture of imers because the nucleophic attack of the thiol occurs from either face of the maleimie. The electron ensity for the sulfur atom, thus, appeare as a population-weighte average of the iastereomers. We moele the sulfur atom to fit the peak of the average ensity of all iastereomers. S

12 Table S. Crystal Parameters, Data Collection, an Refinement Statistics Data Collection Space Group C Unit cell imensions (a,b,c,α,β,γ) 66.7, 5., 8.9, 9, 7., 9 Number of Amino Acis, Atoms Protein: 58, 6, Heteroatoms: 9 Total reflections (Unique reflections) 984 Completeness to.8 Å, to.5 Å 94.5%, 78.8% R merge.6 Mosaicity.3 Signal to noise: Average intensity /.8, 7.55 stanar ev to.8 Å, to.5 Å Molecular Replacement Log likelihoo gain 87.5 R factor 37.8 Refinement Resolution Range / Reflections 5.8, 984 total (67 working set, 3 test set) Number of Amino Acis, Atoms Protein: 58, 6, Heteroatoms: 9 Orere waters seen Free R-factor (%) 4. R factor (%) 6.9 Structural quality statistics Ramachanran plot: #Resiues in core, outliers regions 8, 7 Protein B-factors (mean /- SD).3 /-.7 Waters B-factors (mean /- SD) 6.6 /- 7.5 R merge for replicate reflections = I j I j I, where I j j is the intensity measure for reflection h an <I j > is the average intensity for reflection h calculate from replicate ata. Free R-factor is the R factor calculate only on the % of the reflections that were set asie for cross-valiation an not use in refinement. R-factor = Fo Fc Fo S

13 REFERENCES () rishnamurthy, V. M.; Semetey, V.; Bracher, P. J.; Shen, N.; Whitesies, G. M. J. Am. Chem. Soc. 7, 9, 3. () Leslie, A. G. W. Acta Crystallographica Section D 6, 6, 48. (3) Bailey, S. Acta Crystallogr D 994, 5, 76. (4) im, C.-Y.; Chang, J. S.; Doyon, J. B.; Bair; Fierke, C. A.; Jain, A.; Christianson, D. W. Journal of the American Chemical Society,, 5. (5) Rea, R. Acta Crystallographica Section D, 57, 373. (6) Brunger, A. T.; Aams, P. D.; Clore, G. M.; DeLano, W. L.; Gros, P.; Grosse-unstleve, R. W.; Jiang, J. S.; uszewski, J.; Nilges, M.; Pannu, N. S.; Rea, R. J.; Rice, L. M.; Simonson, T.; Warren, G. L. Acta Crystallogr D Biol Crystallogr 998, 54, 95. (7). Muller, H. J. A., D.M. Doran, P.R. Gerber,. Gubernator, an G. Schrepfer Bull. Soc. Chim. Belg. 988, 97, 655. (8) Aams, P. D.; Pannu, N. S.; Rea, R. J.; Brunger, A. T. Proc Natl Aca Sci U S A 997, 94, 58. S3